I have been finding dr/dt by taking the derivative wrt time of v+pir^2*h and then using dr/dt to find dA/dt by deriving A=pi*r^2. Please Help!

maybe you should post your steps. you're describing the right way to tackle this problem. check your units, and make sure you make the rates negative or positive as appropriate.

November 9th 2010, 06:32 PM

rawkstar

ok so it is given that dV/dt=-5 and that at a certain point d=300 (so r=150), h=0.001, and dh/dt=-0.0002
we know that V=pi*r^2*h so dV/dt=2pi*r*h*dr/dt+pi*r^2*dh/dt
I plugged in dV/dt, h, and dh/dt and got -5=2pi*0.001*r*dr/dt+pi*r^2*-0.0002
since D=300 r=150
-5=300pi*0.001*dr/dt+150^2*pi*-0.0002 so dr/dt=(-5+4.5*pi)/(.3pi)
i also know that A=pi*r^2 so dA/dt=2*pi*r*dr/dt
so i plugged in dr/dt and 150 for r and got
dA/dt=300*pi*[(-5+4.5*pi)/(0.3*pi)]